115 adults were asked whether or not they prefer sodas and whether or not they prefer fruit drinks. The data from the survey is shown in the Venn diagram. How many adults prefer fruit juice?
How many adults do not prefer soda and do not prefer fruit juice?
How many adults prefer fruit juice and prefer soda?
How many adults prefer soda and do not prefer fruit juice?

(08.01)consider the following pair of equations: x + y = −2 y = 2x + 10 if the two equations are graphed, at what point do the lines representing the two equations intersect? (−4, 2) (4, 2) (−2, 4) (2, 4)

Use the four functions below for this question. compare and contrast these four functions using complete sentences focus on the slope and y- intercept first, and then on any additional properties of each function

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis. 3- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in part b?